MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  elima Unicode version

Theorem elima 5347
Description: Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 19-Apr-2004.)
Hypothesis
Ref Expression
elima.1
Assertion
Ref Expression
elima
Distinct variable groups:   ,   ,   ,

Proof of Theorem elima
StepHypRef Expression
1 elima.1 . 2
2 elimag 5346 . 2
31, 2ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  e.wcel 1818  E.wrex 2808   cvv 3109   class class class wbr 4452  "cima 5007
This theorem is referenced by:  elima2  5348  rninxp  5451  imaco  5517  isarep1  5672  eliman0  5900  funimass4  5924  isomin  6233  dfsup2  7922  dfsup2OLD  7923  dfac10b  8540  hausmapdom  20001  pi1blem  21539  adjbd1o  27004  brimage  29576  dfrdg4  29600  tfrqfree  29601  dfint3  29602  imagesset  29603  elimaint  37764  elintima  37765
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017
  Copyright terms: Public domain W3C validator